## How to learn about basic FEM concepts

spacedout
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Joined: 30 Mar 2020, 23:27
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### How to learn about basic FEM concepts

Hi

Q1.
What is the mathematical or physical meaning of permutations in the Elmer code - the following crops up everywhere:
Solver % Variable % Perm

Q2.
Because of the pandemic, my library is closed and I dont have access to the references [3] Szabo & Babuska , [4] Solin et al listed at the end of appendix E of ElmerSolverManual.pdf Can anybody suggest equivalent free online resources ? That could apply to question 1 above as well.

Regards to all
raback
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### Re: How to learn about basic FEM concepts

Hi

Permutation has several uses. At simplest the size of it is the number of nodes, the value is >0 when the field value is present at a node, and =0 when not. The value is use to order the values, for example to minimize bandwidth of the resulting matrix.

When there are edge, face or bubble degrees of freedom the Permutation vector is longer and controls these dofs in the same way.

As an example the global index of the 1st node in element is Solver % Variable % Perm( Element % NodeIndexes(1) ).

There really is no physical meaning it is just machinery of keeping track of global indexes.

-Peter
spacedout
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Joined: 30 Mar 2020, 23:27
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### Re: How to learn about basic FEM concepts

Thank you ever so much. I am glad to hear that permutations are used for code optimization. I was afraid at first that it had something to do with some deep theoretical knowledge of FEM. Speaking of the latter, I downloaded
THE H, P AND H-P VERSION OF THE FINITE ELEMENT METHOD
BASIC THEORY AND APPLICATIONS 1993 by Dr. Babuska and Dr Guo.
So hopefully, I will now better appreciate appendix E of ElmerSolverManual.pdf